GameCube has been traditionally bound to composite OR crazy expensive component cables UNITL NOW! Metal Jesus reviewed a really awesome GameCube HDMI connector made by zeldaxpro and the interest for them has been so high he can't meet demand right now! Basically zeldaxpro hacked the GameCube digital out port to accept HDMI and apparently makes them by hand at his house, which is why he is having a hard time meeting demand.

This is one of the reasons why I love the retro game community so much because long after the lifespan of a console is over people are still creating really amazing hardware to keep systems going.